Tie the beef with kitchen string to help maintain its shape. Season the beef with salt and pepper. Heat the remaining 1 tablespoon oil in a heavy small skillet over medium heat. Add the beef to the skillet and cook until brown and cooked to desired doneness, about 8 minutes for rare. Freeze the beef until it is just frozen (this will make it easier to slice), about 3 hours. Using a large sharp carving knife, cut the beef into thin slices.

Spread the bell pepper mayonnaise over the crostini and top with the sliced beef. Arrange the crostini on a platter. Scatter over the capers, sprinkle with the coarse sea salt, and serve.

Do-Ahead Tip: The bell pepper mayonnaise and sliced beef can be made 1 day ahead. Cover separately and refrigerate.

Alternative: If desired, the beef tenderloin can be substituted with 1 pound freshly sliced roast beef. Since the roast beef is already cooked and can be used as is, it makes a great time-saving alternative.